Density, also referred to as specific gravity, is an important process variable in liquid phase manufacturing processes. Density is defined as the mass of a material divided by its volume. To date, no good method of continuously monitoring the property exists. Solid state measurements of density that are suitable for in-process measurements either require multiple sensors or prior knowledge of additional material parameters (e.g. compressional elastic modulus or viscosity) or carefully controlled flow properties (e.g. in a coriolis force measurement.
Viscosity and, more generally, viscoelasticity, are properties of liquids and solids that relate the shear forces generated by or applied to a material to the amount of shear deformation or flow. While the present invention applies equally well to viscoelasticity, for the sake of clarity and simplicity, this disclosure will use viscosity as an example, with the understanding the invention extends to other viscoelastic characteristics. Viscosity is of widespread interest in many manufacturing environments and is measured as a primary quality of some products and as a secondary quality (a means of monitoring process state) in other processes. In many of these applications, measurement of density is also a requirement.
Viscosity describes the force required in order to make successive molecular layers of a liquid move past each other at a given rate of shear (“shear rate”). If one considers a liquid flowing past the walls of a container, the liquid will typically have no motion relative to the wall at the interface and will have increasingly higher velocities as one observes points successively further from the wall. The shear rate is defined as the gradient of the velocity of the liquid parallel to the surface (meters per second) with increasing distance from the surface (meters). The units of shear rate are 1/seconds. The shear stress is the amount of force per unit area that must be applied in order to cause the motion.
Hydrodynamic properties of liquids are quantified by the speed of shear sound waves in a liquid. An ideal liquid, having neither shear elasticity nor viscosity, cannot support a shear sound wave. An elastic solid having a shear stiffness, μs, can support a shear acoustic wave that propagates through the solid much as the better known compressional sound wave. The velocity of the wave is (μs/ρs)1/2, where ρs is the solid's density. Viscous liquids can support a shear sound wave; however the wave decays as it travels and is only able to travel a few wavelengths before being totally dampened out by frictional losses. The complex velocity of these waves is (jωη/ρ)1/2=(1+j)(ωη/2ρ)1/2. Measurement of the shear wave velocity thus provides information on the ratio of liquid's viscosity to its density and can thus be used to measure density if viscosity data is available.
These “sound waves” are related to the flow of liquids in confined geometries, such as capillaries, pipes and the spaces between moving parts in machinery. These flows are governed by the ratio of the intrinsic viscosity, η, to the density of the material, ρ. The ratio is known as the “kinematic viscosity”, ηk=η/ρ, and has the units of area over time (m2/s).
There exist densitometers which measure changes in the resonant frequency of a tuning fork as it is filled with the test liquid. The method is highly susceptible to vibration. It is an object of the present invention to provide a sensor that is immune to most vibration levels. One method of reducing susceptibility to vibration while employing the resonant measurement method is to employ a high frequency (MHz) resonator, such that the vibrations are well outside the frequency band of the instrument.
Compressional acoustic wave devices measure the product of elastic modulus and density (acoustic impedance) or the ratio therebetween (acoustic velocity) and offer one potential avenue of obtaining both values from a single “measurement”. However, the complexity of the structure and of the signal analysis has severely limited this approach for transmission based systems (acoustic spectroscopy). Typically these systems employ pulse echo systems in which a signal undergoes multiple transmissions through the test sample. The systems are extremely dependent on accurate knowledge of the path length in the sample. A preferred solution would employ a single point of contact and localized measurement.
Tuning fork methods measure the product of density and elastic modulus or the product of density and viscosity and are presently sold as densitometers. They attribute downward shifts of the resonant frequency to density (ignoring elastic modulus) and decreases in resonant quality factor (increased damping) to the viscosity-density product. The methods require prior knowledge of the elastic modulus and careful control of the depth of insertion of the tuning fork into the sample. A method is desired in which the depth of insertion is not critical and in which no other parameter need be known other than those measured by the sensor itself, or a small number of other sensors that may be coupled within a limited area or enclosure, to provide data on localized conditions.
In addition to the propagation of acoustic waves through a material, it is possible to employ acoustic waves in an adjacent solid to measure the power transfer into the viscous liquid. Power transfer from one medium to the other is governed by the ratio of the acoustic impedances of the materials. Power transfer of acoustic energy between a solid waveguide and an adjacent liquid forms the basis of several viscometers. The rate of energy transfer (power loss) is dependent on the relative acoustic impedances of the waveguide material and the adjacent liquid in a manner well-known to one skilled in the art. The acoustic impedance of the shear wave in the solid waveguide is the square root of the product of the density, ρs, and the shear elastic stiffness, μs. It is predominantly real (resistive) and is analogous to a nearly-lossless transmission line's characteristic impedance in electromagnetics. The acoustic impedance of a shear wave in a viscous liquid is the square root of the product of the stiffness term, jωη, with the density, ρ. The characteristic impedance of the viscous liquid is typically very small compared to the elastic solid, resulting in a low power transfer. At low viscosity the power transfer is proportional to (ωρη)1/2. Therefore, if the viscosity is known, density can be measured.
U.S. Pat. No. 5,708,191 Greenwood et al., U.S. Pat. No. 5,886,250 Greenwood et al., U.S. Pat. Nos. 6,082,180 and 6,082,181 to Greenwood, present a family of densitometer sensor designs that employ input and output transducers to measure changes in reflected signal strength of acoustic waves as they reflect near a critical angle of incidence. These viscometers measure either viscosity-density product or elasticity-density product based on the reflection of acoustic waves from the liquid-loaded face of a solid material supporting the transducers. The sensors measure reflection coefficients of the wave from solid-liquid boundaries upon a few reflection events of a pulsed or continuous-wave signal. Such methods offer less sensitivity and resolution of the measured quantity than do resonant and multi-reflective devices. The latter enjoy higher sensitivity from the continuous interaction of their acoustic waves with the solid-liquid interface. The discrete-reflection methods do not enjoy the simplicity of manufacture or operation of a continuous acoustic wave interaction surface, nor do they provide similar sensitivity or resolution. Finally, the discrete reflection methods assume a fixed elastic modulus (for the more common compressional wave version) or viscosity (for the less common shear wave version) in order to extract density information from the measured response of the sensor.
Another method of performing the density-viscosity product measurement is to immerse a resonator manufactured on a piezoelectric substrate and supporting a transverse shear mode of resonance, typically a disc of quartz crystal of AT cut, into the liquid and to measure the shift in resonant frequency or the loss of power at resonance. This method has been plagued by poor reproducibility when used with affordable instrumentation, primarily due to the lack of a differential measurement within the sensor.
This issue has been overcome through the use of two-port devices based on multi-pole resonators using shear wave acoustic modes, such as the SH-SAW (Shear Horizontal-Surface Acoustical Wave), SHAPM (Shear Horizontal Acoustical Plate Mode), MPS (Monolithic Piezoelectric Sensor) e.g. as described in U.S. Pat. No. 6,033,852, issued Mar. 7, 2000 to Andle et al.
U.S. Pat. Nos. 5,741,961 and 5,798,452 to Martin et al. disclosed a method in which two acoustic wave sensors having different surface treatment exhibit essentially identical responses to viscosity-density product but differing responses to the density. A reference sensor provides data on the product of viscosity and density and employs a smooth surface. The second sensor has an intentionally roughened surface, typically having grooves or pits in its surface for trapping a certain volume of fluid. The added mass creates a finite frequency shift with little or no power loss in addition to the power loss and frequency shift of the viscously entrained liquid. The difference in the frequency shifts between the two sensors is therefore attributed to the mass of the material trapped in grooves or wells of a textured surface, providing a measure proportional to the density via the frequency difference. The density-viscosity product is available via the common-mode frequency shift. While this method is attractive, it incurs difficulties in sensor-to-sensor reproducibility when the two sensors are manufactured on different substrates.
The addition of such grooves to one of a pair of shear horizontal surface acoustic wave (SH-SAW, also known as Love Wave, surface transverse wave, and the like.) sensors is also disclosed (Herrmann et al., U.S. Pat. No. 6,543,274), and the extension of this approach to SHAPM sensors is contemplated herein. This method offers higher frequency, smaller size, and improved sensitivity at the expense of manufacturing complexity and available dynamic range. However Herrmann still finds the use of two completely identical sensor elements necessary for measuring both parameters, and therefore it does not overcome the sensor-to-sensor limitations of the Martin device.
In a U.S. Pat. No. 7,007,546 to Andle titled “Measurement, Compensation and Control of Equivalent Shear Rate in Acoustic Wave Sensors” (which is incorporated herein by reference in its entirety), the inventor of the present application disclosed a method for measuring viscosity and shear rate at which the measurement is performed by utilizing an acoustic wave sensor, and calculating the shear rate as a function of the characteristic rate of fluid movement in response to a given power transmitted to a fluid, and the viscosity of the fluid. The acoustic wave device has a characteristic relationship between input power, output power, and an acoustic wave amplitude at a selected region between the input and output transducer. The acoustic wave device is coupled to the measured fluid. A predetermined power level Pin of a harmonic signal is applied to an input transducer, to impart an acoustic wave at the selected region. Output power level Pout is measured at the output transducer. Using the characteristic relationship, and the input and output power levels, the amplitude of the average acoustic wave imparted to the fluid is calculated. Measuring the viscosity of the fluid to obtain a measured viscosity at the selected region, allows calculating of the shear rate of the fluid at the selected region, by using the frequency, the viscosity measurement, and the acoustic wave amplitude. This invention may be beneficially used with the present invention as explained below.
There is therefore a clear and unanswered need for a densitometer, and also for a combination densitometer/viscosity meter, that is reliable, precise, easy to manufacture, and easy to install in various applications, which does not rely necessarily on the use of a plurality of sensors and that is compensated for wide variations in the viscosity of the sample. The preferred embodiments of the present invention provide such solutions.